Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number Hook - Magic Trick

7 minutes

Since my students have been working with subtraction, I start this lesson by showing a quick subtraction trick. I tell students that I can calculate the difference between 1000 and a three digit number within 4 seconds.

Subtracting from 1,000

Step1:To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10:

Step2:Ex:1000-648

Step3: subtract 6 from 9 = 3

Step4: subtract 4 from 9 = 5

Step5: subtract 8 from 10 = 2

Answer: 352

This is a trick in which I ask students how they think I can come up with the answer so quickly. I do several repetitions for them and write a horizontal number sentence on the board as I'm solving the difference. I have always had one student able to verbalize the pattern of 9, 9, 10 when regrouping 1000. Once this is told and I do one more on the board, speaking aloud what my brain is thinking, students are delighted that they too can do this trick. I then spend a little bit of time referring back to Math Practice 8. I remind students that mathematicians notice if calculations are repeated, and look both for general methods and for shortcuts. I over emphasize that I'm not magic, but that I've observed repeated calculations and patters and therefore am able to to perform this computation very quickly as a shortcut. I want my students to walk away feeling like they too can perform this shortcut and amaze their friends and family and through hard work and practice they can be just as fast as me.

Warm Up

7 minutes

Students will start today's lesson with a fluency assessment. This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results. It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions. (It also happens to be the quietest time in my math classroom all week as you can see in the short video below.)

I do not start my students with the fourth grade skills. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. In this book, the fourth grade assessments begin with 25 problems that include double digit by double digit multiplication and long division. Since these are both concepts I don't present to students until October and November, I 'd rather have my students working on fluency with the four operations for problems they have familiarity with. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards. By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics. I want to make clear that this assessment ONLY measures basic math computation. It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year. Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.

Concept development

Students will work in small groups today to play games that reinforce multiplication facts, (unit begins next week), and place value as well as have time with me in a smaller setting.

During this lesson, I work with a small group of students to complete the additive comparison problems sheet (additive compare problems) to work at mastering standard 4.OA.2. I do not print the practice page for this lesson because I want students to talk with each other and with me about the word problems. I use my document camera to display the page as we sit on the floor and work and talk about the problems together in the group.

This photo is of that small group of students solving a problem that is displayed on the whiteboard.

The problems on the practice page can be tricky for students because students often miss the last step. Many students will subtract the numbers, but then fail to recognize they haven't necessarily answered the question. Knowing this, I wanted to be able model problems and guide my students through questioning. Often, all I need to do is says something like, (for number 3) "So, you're telling me the male hippo weighs _____MORE?" When I emphasize the language some students are able to identify they haven't answered the question and then can complete the next step independently.

In this place value unit, I have done many whole group lessons, and partner work with word problems. I chose small group work today because I wanted to make sure I could talk and connect with every student, listening to their thinking in order to make instructional decisions.

When students are not in small group work, they play one of two different games I assign them to: Multiplication War or Place Value Snap. The directions for these games are located in the resource section.

Note: One thing I had to state several times and re-state at various points in the math lesson was that students playing the games needed to WHISPER. For some teachers, this lesson would have been too much noise in the classroom. I am a teacher that has grown to love noise in the classroom as long as it is math-speak. My students know that as long as they are talking math and staying on task, I expect them to talk to each other, learn from each other, and help each other. Games add a different level of noise intensity to the classroom, but these games are so beneficial for student engagement and learning.

I chose Multiplication War as a game today because the next unit I will present to students is multiplication and division. Many of my students do not have their basic multiplication or division facts mastered and need more time and practice to memorize them. As stated in the common core standards, by the end of Grade 3, students will know from memory all products of two one-digit numbers. For the majority of my students, this game allows them to practice their basic multiplication facts in fun way and work at memorizing these facts.

These two students are playing multiplication war.

I chose the second game, Place Value Snap because I wanted to challenge several students who already have their basic facts mastered and have many of the concepts from this place value unit mastered. For this reason, I assigned which game students played today. Place Value Snap can be less challenging when students do not need to regroup any places, but I wanted my students to play with regrouping, making a very cognitively demanding, but engaging game.

You can see in this photo, the group of students using a whiteboard and place value chart as tools to help them figure out the number name of the number they have created.

I loved seeing the place value chart as a tool they had decided to use. I wasn't certain if this group would be able to regroup and name the number mentally. Seeing them use a tool we have practiced made my heart smile and proved to also be beneficial for them in figuring out their number too.

The following paragraph is information I found helpful in thinking about standard 4.OA.2 and designing this lesson.

"When distinguishing multiplicative comparison from additive comparison, students should note that additive comparisons focus on the difference between two quantities (e.g., Deb has 3 apples and Karen has 5 apples. How many more apples does Karen have?). A simple way to remember this is,“How many more?” Multiplicative comparisons focus on comparing two quantities by showing that one quantity is a specified number of times larger or smaller than the other (e.g., Deb ran 3 miles. Karen ran 5 times as many miles as Deb. How many miles did Karen run?). A simple way to remember this is “How many times as much?” or “How many times as many?

Student debrief - Wrap Up

2 minutes

This lesson was almost a bell ringer, going right up to the very last minute. I did save 2 minutes for a quick thumbs up, thumbs down activity. I ask the students various questions and they show me a thumb up if they like it or agree, or a thumbs down if they don't agree or didn't like something. I let my students do a thumb sideways if they can't decide or haven't decided yet.